Therefore, it appears difficult to analyze function derivatives evaluated at a fixed point, as existing work on the plug-in property typically assumes the functional to be bounded [1]}, [2]}, [3]}. In addition, differential operator that maps a function to its derivative functions have a wide range of applications in statistics [4]}, [5]}; they point to function-valued functionals, or nonparametric functionals, as oppose to real-valued functionals that are considered in the classical plug-in property literature. As such, we generalize the plug-in property for real-valued functionals to function-valued functionals, and term it as nonparametric plug-in property.
